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Require Import Omega.
Lemma lt_2xp1 : forall x i : nat, i < x -> 1 + 2 * i < x + x.
Proof.
intros; omega.
Qed.
Lemma lt_2xp : forall x i : nat, i < x -> 2 * i < x + x.
Proof.
intros; omega.
Qed.

Keybase proof

I hereby claim:

  • I am hackedy on github.
  • I am hackedy (https://keybase.io/hackedy) on keybase.
  • I have a public key whose fingerprint is 9426 17BA 6D4A A5DE EF90 6DC0 DC9C 5256 3A8A 79C8

To claim this, I am signing this object:

no_parens:
== disasm: <RubyVM::InstructionSequence:block in <main>@weird.rb>=======
== catch table
| catch type: break st: 0004 ed: 0007 sp: 0000 cont: 0007
| catch type: redo st: 0000 ed: 0009 sp: 0000 cont: 0000
| catch type: next st: 0000 ed: 0009 sp: 0000 cont: 0009
|------------------------------------------------------------------------
0000 trace 256 ( 1)
0002 trace 1
0004 putself
.<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<!--
. .o8 oooo
.o8 "888 `888
.o888oo oooo oooo ooo. .oo. .oo. 888oooo. 888 oooo d8b
888 `888 `888 `888P"Y88bP"Y88b d88' `88b 888 `888""8P
888 888 888 888 888 888 888 888 888 888
888 . 888 888 888 888 888 888 888 888 888 .o.
"888" `V88V"V8P' o888o o888o o888o `Y8bod8P' o888o d888b Y8P
/***********************************************
* Floating image script- By Virtual_Max (http://www.geocities.com/siliconvalley/lakes/8620)
* Modified by Dynamic Drive for various improvements
* Visit Dynamic Drive at http://www.dynamicdrive.com/ for full source code
* Modified again by hackedy (hackedy.tumblr.com) to be less incredibly shitty
**********************************************/
var vmin = 2;
var vmax = 5;
var vr = 2;
@hackedy
hackedy / Brainfuck.hs
Created August 21, 2012 05:22
BRAINFUCK
-- a brainfuck interpreter in haskell. woohoo.
--
-- as a refresher: operators in brainfuck:
--
-- > increment data pointer
--
-- < decrement data pointer
--
-- + increment the byte at the data pointer
--
#define LENGTH 4096
#include <stdlib.h>
void main(void) {
char *x = malloc(LENGTH);
x[LENGTH] = '\0';
puts(x);
int i;
for (i = 0; i < LENGTH; i++) {
putchar((int)(x[i]));
}
@hackedy
hackedy / gist:1088588
Created July 18, 2011 05:06
V8 bundled with Node.js doesn't build with gcc 4.6 and -Werror
% make
Waf: Entering directory `/home/ryan/d/code/node/build'
DEST_OS: linux
DEST_CPU: ia32
Parallel Jobs: 1
Product type: program
[ 1/33] copy: src/node_config.h.in -> build/default/src/node_config.h
[ 2/33] copy: tools/nodejs.pc.in -> build/default/tools/nodejs.pc
[ 3/33] cc: deps/http_parser/http_parser.c -> build/default/deps/http_parser/http_parser_3.o
/usr/bin/gcc -rdynamic -pthread -m32 -g -O3 -DHAVE_OPENSSL=1 -DHAVE_MONOTONIC_CLOCK=1 -D_LARGEFILE_SOURCE -D_FILE_OFFSET_BITS=64 -DHAVE_FDATASYNC=1 -DARCH="ia32" -DPLATFORM="linux" -D__POSIX__=1 -Wno-unused-parameter -D_FORTIFY_SOURCE=2 -Idefault/deps/http_parser -I../deps/http_parser ../deps/http_parser/http_parser.c -c -o default/deps/http_parser/http_parser_3.o
@hackedy
hackedy / DIP.py
Created June 29, 2011 03:15 — forked from Senix/DIP.py
#!/usr/bin/python
#Download all sluggy freelance images
import urllib
mage = int(raw_input('image to download: '))
mage += 1
lett = 'a'
imagetype = '.gif'
filename = "%s%s.gif" % (mage, lett)